\((2x - 9) + (3x - 6) = 110\)
\(2x + 3x - 9 - 6 = 110\)
\(5x - 15 = 110\)
Plus sides 15
\(5x - 15 + 15 = 110 + 15\)
\(5x = 125\)
Divided sides by 5
\( \frac{5}{5}x = \frac{125}{5} \\ \)
\(x = 25\)
Thus ;
A = 2 ( 25 ) - 9°
A = 50° - 9°
A = 41°
_________________________________
B = 3 ( 25 ) - 6
B = 75° - 6°
B = 69°
_________________________________
C + 110° = 180°
because it is a straight line.
Subtract sides 110°
C + 110° - 110° = 180° - 110°
C = 70°
_________________________________
And we're done.....♥️♥️♥️♥️♥️
Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
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HELP plsssss
A house painting company charges $350 plus $15 per hour. Another company charges $275 plus $20 per hour. Write an equation that represents when both companies will cost the same amount. How long will the job be when both companies charge the same amount? How much will they charge?
Question 1: Write an equation.
Question 2: How long will the job be when both companies will cost the same amount?
Question 3: How much will they charge?
Answer:
BelowI hope it helps ♥Step-by-step explanation:
1. Equation representing when both companies will cost the same amount :
\(350 + 15x = 275 + 20x\)
2. Let x equal the number of hours a job takes , then the first house painting company will charge 350+15x , the second house painting will charge 275 +20x. If the two companies charge the same amount , we will have;
\(350 +15x = 275+20x\\\\350 - 275 = 20x - 15x\\\\75 = 5x\\\\\frac{75}{5} = \frac{5x}{5} \\\\15 = x\\\\x = 15\:hours\)
3. For a job that takes 15 hours , the first company will cost ;
\(350 + 15(15) = 575\)
For a job that takes 15 hours , the second company will cost ;
\(275+20x\\\\275+20(15)\\\\275 +300\\\\=575\)
Question in picture solve
Answer:
5
Step-by-step explanation:
10/2=5
20/4=5
hope this helps :3
if it did pls mark brainliest
Answer:
1:5
Step-by-step explanation:
30 divided by 6 is 5 and so are the rest
Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer. A used Car salesperson can be paid using two methods of commission. METHOD X uses straight commission 3.5% of the selling price of all vehicles sold. METHOD Y uses a fixed amount of £250 per week plus commission of 1.5% of the selling price of all vehicles sold. If the total selling price of the Cars sold in each week is on average £20,000, calculate which of the two methods of commission the salesperson would prefer.
The cost of one computer is £600 and the cost of one printer is £800.
Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.
Let the cost of a computer be x and the cost of a printer be y.
Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)
4x + 5y = 6000 ---------------------- (2)
Solving equations (1) and (2) simultaneously:x = 600y = 800
Therefore, the cost of a computer is £600 and the cost of a printer is £800..
:Therefore, the cost of one computer is £600 and the cost of one printer is £800.
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I don’t know how to find the value of x PLEASE HELP!!!
Answer:
the value of x is 8.
Step-by-step explanation:
\(x {}^{2} = 64\)
\(or \: x = \sqrt{64} \)
therefore x=8
is the answer...
Answer:
x=8
Step-by-step explanation:
\(8^{2} =64\)
8·8·8·8·8·8·8·8=64
hope this helps
good luck!!
Pls answer 40pts Drag the tiles to the correct boxes to complete the pairs.
Match each quadratic function to its graph.
f(x) = -2(x + 3)2 − 1
f(x) = -2(x + 3)2 + 1
f(x) = 2(x + 3)2 + 1
f(x) = 2(x − 3)2 + 1
Answer:
Step-by-step explanation:
f(x) = -2(x+3)^2 -1 would be the fourth graph because its translated 3 to the left, negative, and 1 down
f(x)=2(x+3)^2+1 would be the first graph since it's translated 3 to the left, positive, and shifted 1 up
f(x)=-2(x+3)^2+1 would be the second graph since it's translated 3 to the right, negative, and shifted 1 up
f(x)=2(x-3)^2+1 would be the third graph since it's translated 3 to the right, positive, and shifted 1 up
The table below shows the annual profit for five companies, the cost to purchase that company and the number of employees currently employed. If the profit per employee remained the same, how many extra employees would Company C have to employ to achieve an annual profit that is 250% more than the current one?
Company C would need to employ an additional 70 employees to achieve an annual profit that is 250% more than the current one.
To achieve an annual profit that is 250% more than the current one, Company C needs to increase its profit by 250% of its current profit, which is $200,000.
This gives us a target profit of $700,000. Since the profit per employee remains the same, we can find the number of additional employees needed by dividing the target profit by the profit per employee and subtracting the current number of employees.
Number of additional employees = (Target profit / profit per employee) - Current number of employees
For Company C, the profit per employee is $10,000 ($200,000 / 20), so the number of additional employees needed is:
(Number of additional employees) = ($700,000 / $10,000) - 20 = 70
Therefore, Company C would need to employ an additional 70 employees to achieve an annual profit that is 250% more than the current one.
Note: The cost to purchase the company and the number of employees currently employed are not relevant to this calculation.
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The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms
The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.
The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.
We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)
B = 32 m²
When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.
Divide the mass by the volume to get the density, or D = M/V.
According to values,
19.3 = M/448
M = 8646.4 grams, which is equal to 8.646 grams.
The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.
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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.
How do you write an equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4?
The equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)
It is given that,
y=2x-4
We have to write an equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4.
The slope of the given equation,
y=2x-4
m=2
The slope of the parallel lines is equal,
m=2
The equation of a line that passes through the point (5,-1) with slope 2 is,
y-y₁=m(x-x₁)
y-(-1)=2(x-5)
y+1=2(x-5)
y+1=2x-10
y=2x-11
Thus, the equation of a line that passes through the point (5,-1) and is parallel to the line y=2x-4 will be y=2x-11.
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3.
A soccer ball travels upward from a height of 11 feet with an initial velocity of 20
feet per second. The quadratic function h (t) = -16t² + 20t + 11 models the height
of the ball, where h (t) is the height, in feet, of the soccer ball and t is the time that
ball has been in the air, in seconds. When is the soccer ball above 15 feet?
A. The soccer ball is above 15 feet between 0 seconds and 0.5 second.
B. The soccer ball is above 15 feet between 0.5 second and 1 second.
C. The soccer ball is above 15 feet between 0.25 second and 1 second.
D. The soccer ball is above 15 feet between 0 seconds and 0.25 second.
m
The square of a real number is always non-negative, there are no values of t that satisfy the inequality. Therefore, the soccer ball is never above 15 feet.
The correct answer is none of the given options (A, B, C, or D).
To determine when the soccer ball is above 15 feet, we need to find the values of t that satisfy the inequality h(t) > 15.
Given the quadratic function h(t) = -16t² + 20t + 11, we can set up the inequality:
-16t² + 20t + 11 > 15
Rearranging the inequality:
-16t² + 20t - 4 > 0
Dividing both sides by -4 to simplify:
4t² - 5t + 1 < 0
To solve this quadratic inequality, we can factorize it:
(2t - 1)(2t - 1) < 0
(2t - 1)² < 0
Since the square of a real number is always non-negative, there are no values of t that satisfy the inequality. Therefore, the soccer ball is never above 15 feet.
The correct answer is none of the given options (A, B, C, or D).
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a movie ticket is $12.00, plus an 8.5% sales tax. How much will one movie ticket cost
Answer: the ticket cost will be 13.02
Step-by-step explanation:
first, find the %8.5 out of 12 which is 1.02, and then add 12 + 1.02
what is the solution to the equation below sqrt x-2 = x-22
Answer:
√27-2 =27-22
√25. =5
the answer is option B
x=27
Answer:
option B : x = 27
Step-by-step explanation:
Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $850 and $65, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 460) and (10, 200)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (200 - 460)/(10 - 6)
Evaluate
Rate = -65
This means that the rate of change is -$65
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = -65
So, we have
y = -65(x - x1) + y1
Using one of the points, we have
y = -65(x - 10) + 200
Set x = 0
So, we have
y = -65(0 - 10) + 200
Evaluate
y = 850
Hence, the initial amount and rate of change given a table for a linear function are $850 and $65, respectively
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Simplify the following expressions:
5x + 4 + (-x) -1
Answer:
\(4x+3\)
Step-by-step explanation:
\(5x+4+(-x)-1\)
Remove parentheses: \((-a)=-a\)
\(=5x+4-x-1\)
Group like terms
\(=5x-x+4-1\)
Add similar elements: \(5x-x=4x\)
\(=4x+4-1\)
Add/subtract the numbers: \(4-1=3\)
\(=4x+3\)
9) Write down the mean and variance of a binomial random variable with n trials and success probability p. g
The mean and variance of a binomial random variable with n trials and success probability p are np and np(1-p), respectively.
The mean and variance of a binomial random variable with n trials and success probability p are given by the following formulas:
Mean = np
Variance = np(1-p)
Where n is the number of trials and p is the probability of success in each trial.
To understand this better, let's consider an example. Suppose we conduct an experiment where we toss a coin 10 times and we want to know the probability of getting exactly 5 heads.
This is a binomial experiment because there are only two possible outcomes (heads or tails) and each trial is independent of the others. The probability of getting a head on any given trial is 0.5.
Using the formula for the mean, we get:
Mean = np = 10 x 0.5 = 5
This means that on average, we can expect to get 5 heads out of 10 tosses.
Using the formula for the variance, we get:
Variance = np(1-p) = 10 x 0.5 x (1-0.5) = 2.5
This means that the spread of the distribution is relatively large, indicating that there is a significant amount of variability in the number of heads we can expect to get.
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One side of an equilateral △PQR on the ordinate plane at point P (-3,2) and Q (5,2). What is the coordinate of vertex R?
The point R must also have a y-coordinate of 2. Since R is equidistant from P and Q,
Since △PQR is equilateral, we know that all three sides are congruent. Therefore, the distance between points P and Q is equal to the distance between points P and R or Q and R.
The distance between P and Q is 8 units (5-(-3) = 8), so the distance between P and R or Q and R must also be 8 units.
Since the triangle is equilateral, the point R must be located on a line that is equidistant from points P and Q. This line is the horizontal line passing through the midpoint of PQ.
The midpoint of PQ is ((-3+5)/2, (2+2)/2) = (1,2). Therefore, the point R must also have a y-coordinate of 2.
Since R is equidistant from P and Q, it must lie on the vertical line passing through the midpoint of PQ. This line is the line x = 1. Therefore, the coordinate of vertex R is (1,2).
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what about two and nine hundredths?
Answer:
2.09 is the answer now what
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
the amount of medication, in milligrams, in a patient's bloodstream after t hours, can be represented by the following function: m of t equals 88 over the quantity 1 plus e to the x plus 7 tenths power end quantity what is the rate of change for the amount of medication in the patient's bloodstream after 4 hours?
Answer:
about -0.79 mg/hour
Step-by-step explanation:
You want the rate of change of the amount of medication in a patient after 4 hours if the amount after t hours is modeled by y=88/(1+e^(t+0.7)).
Rate of changeThe rate of change is found by taking the derivative of the function with respect to time. Let u = 1+e^(t+0.7). Then du/dt = e^(t +0.7).
The function can be written ...
y = 88/u = 88·u^-1
so its derivative is ...
dy/dt = (-88·u^-2)·du/dt
dy/dt = -88(e^(t +0.7))/(1 +e^(t +0.7))^2
At t=4The value of the rate of change at t=4 is ...
dy/dt = -88(e^(4 +0.7))/(1 +e^(4 +0.7))^2 ≈ -88(109.95)/(1 +109.95)^2
dy/dt ≈ -0.78602 ≈ -0.79 . . . . . . mg/h
The rate of change in the amount of medication is about -0.79 mg/h.
a physician uses two labs to measure patient cholesterol levels and believes that lab 1 (1) may be reporting lower cholesterol levels, on average, than lab 2 (2). to test their theory, the physician collects pairs of blood samples from 35 patients and sends a sample from each patient to lab 1 and sends the other sample from each patient to lab 2. from the 35 pairs of blood samples, the mean and standard deviation of differences in cholesterol levels are calculated. is there evidence to confirm that lab 1 is reporting lower cholesterol levels, on average, than lab 2? flag question: question 9 question 9 5 pts which type of test should be used to determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2? group of answer choices paired t test for means paired z test for means z test for means sign rank test t test for proportions t test for means z test for proportions
To determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2, a paired t-test for means should be used.
This is because the physician collected pairs of blood samples from each patient and wants to compare the means of the two labs' cholesterol level measurements. The paired t-test for means is appropriate for comparing the means of two related samples, in this case, the blood samples from each patient tested by lab 1 and lab 2.
A paired t-test for means should be used to determine if lab 1 is reporting lower cholesterol levels, on average, than lab 2. This test is appropriate because the data consists of paired samples from the same patients, and the goal is to compare the means of the differences between the two labs.
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What is the mathematical expression for modified Reynolds Analogy, also known as Chilton-Colburn analogy?
The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.
The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.
The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.
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Find the perimeter of HIJ
Answer:
110 units
Step-by-step explanation:
Triangles EFG and HIJ are similar triangles.
∴ \(\frac{IJ}{FG} =\frac{HJ}{EG}\) (corresponding sides of similar triangles)
\(\frac{IJ}{11} = \frac{45}{18}\)
∴ IJ = 27.5
∴ Perimeter of triangle HIJ
= 27.5 + 37.5 + 45
= 110 units
2x +2y =10 5x -2=4
What is the solution of the system of equations?
A (3,2)
B (2,3)
C (-2,-7)
D(2,7)
12
11
10
9
8
7
6
5
4
3
2
1
A(4,2)
B(9, 10)
1 2 3 4 5 6 7 8 9 10 11 12
OA. 13 units
OB. About 3.6 units
C. 89 units
OD. About 9.4 units
Answer:
D
Step-by-step explanation:
calculate the length of AB using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = A (4, 2 ) and (x₂, y₂ ) = B (9, 10 )
AB = \(\sqrt{(9-4)^2+(10-2)^2}\)
= \(\sqrt{5^2+8^2}\)
= \(\sqrt{25+64}\)
= \(\sqrt{89}\)
≈ 9.4 ( to 1 decimal place )
9. If f(x)=-2x^2+4x-6,
then f(2)=
Answer:
f(2) = -6
General Formulas and Concepts:
Order of Operations: BPEMDAS
Substitution and Evaluation
Step-by-step explanation:
Step 1: Define
f(x) = -2x² + 4x - 6
f(2) is x = 2
Step 2: Solve
Substitute: f(2) = -2(2)² + 4(2) - 6Exponents: f(2) = -2(4) + 4(2) - 6Multiply: f(2) = -8 + 8 - 6Add: f(2) = -6krytine has a weekend job advertising an upcoming play. she has two options for being paid. Option A is an hourly wage of $7.50 Option B is 5% commission on all money made at the play. she plans to work 7 hours each day on Saturday and Sunday. krystine estimates the play will make about $2,000 this weekend. Which option gives more earnings this weekend?
The Answer is: The hourly rate option of $112 is higher than the commission rate of $105.
Step-by-step explanation:
She will work 16 hours at $7.00 per hour:
16 * 7 = $112
Or she could take the 5% commission on $2,100:
2100 * .05 = $105.
The hourly rate is higher than the anticipated commission amount.
please help me with these four questions
Answer:
23) 8
24)58
25)im guessing theyre both 90
Step-by-step explanation:
23)if ac=23 then 15-23=x
24) since it's a 90 degree angle the 32+x=90
and 90-32=58
sally works for 38 hours per week
her weekly wage is £355.68
she receives a pay increase of 23p per hour
work out her new weekly wage
give you're answer in £
It's 38*23 =874 dollars
y = 4x + 8; y = –x + 3
Answer:
y= -12
Step-by-step explanation:
4x+8 = -x+3 -> Find x by using all information
5x=-5 -> Simplify
x=-1 -> Solve
y=-12 -> Plug in to find y
Why is it important to center the x value before squaring? Because X-squared is strongly correlated with Because squaring the x values without centering them first reduces the effects of multicollinearity Because the residual plot needs to have a distinct pattern Because centering the x values will straighten the curve of the scatterplot
Centering x values before squaring eliminates the correlation between x and its square term, reducing multicollinearity. This helps to determine independent effects of predictor variables, and can also straighten the curve of a scatterplot.
Centering the x values before squaring is important because it helps to eliminate the correlation between the x variable and its square term. When we square a variable without centering it, we are essentially capturing the effect of both the linear and the quadratic terms.
This can lead to multicollinearity, which occurs when two or more predictor variables are highly correlated with each other.
Multicollinearity can create problems in statistical analyses because it can make it difficult to determine the independent effects of each predictor variable on the outcome variable. Centering the x values before squaring helps to reduce the effects of multicollinearity by eliminating the correlation between the x variable and its square term.
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